摘要
设G是有限群,子群H称为G的CAP^*-子群,如果H覆盖或者避开G的每个非-Frattini主因子。子群H称为G的几乎CAP^*-子群,如果存在G的次正规子群K使得HK=G,且H∩K是G的CAP^*-子群。本文应用G的某些素数幂阶几乎CAP^*-子群刻画有限群的p-超可解性,推广了相关文献的一些结果。
A subgroup H of a finite group G is called a CAP^*-subgroup of G,if H either covers or avoids every non-Frattini chief factor of G.A subgroup H of G is said to be a nearly CAP^*-subgroup of G if there exists a subnormal subgroup K of G such that HK=G and H∩K is a CAP^*-subgroup of G.This paper investigates the structure of G under the assumption that certain subgroups of prime power orders are nearly CAP^*-subgroups of G,and a series of known results are generalized.
作者
钟祥贵
孙悦
吴湘华
ZHONG Xianggui;SUN Yue;WU Xianghua(College of Mathematics and Statistics,Guangxi Normal University,Guilin Guangxi 541006,China)
出处
《广西师范大学学报（自然科学版）》
CAS
北大核心
2019年第4期74-78,共5页
Journal of Guangxi Normal University:Natural Science Edition
基金
国家自然科学基金(11261007)
广西自然科学基金(2014GXNSFAA118009)
作者简介
通信联系人:钟祥贵(1963-),男,湖南武冈人,广西师范大学教授。E-mail:xgzhong@gxnu.edu.cn。
